Synopsis for C8.1b: Mathematical Physiology

Level: M-level Method of Assessment: Written examination.
Weight: Half-unit (OSS paper code 2B81).

Recommended Prerequisites

B8a highly recommended.

Overview

The course aims to provide an introduction which can bring students within reach of current research topics in physiology, by synthesising a coherent description of the physiological background with realistic mathematical models and their analysis. The concepts and treatment of oscillations, waves and stability are central to the course, which develops ideas introduced in the more elementary B8a course. In addition, the lecture sequence aims to build understanding of the workings of the human body by treating in sequence problems at the intracellular, intercellular, whole organ and systemic levels.

Synopsis

Review of enzyme reactions and Michaelis–Menten theory. Trans-membrane ion transport: Hodgkin–Huxley and Fitzhugh–Nagumo models.

Excitable media; wave propagation in neurons

Calcium dynamics; calcium-induced calcium release. Intracellular oscillations and wave propagation.

The electrochemical action of the heart. Pacemakers, phase oscillators and the sinoatrial node. Spiral waves, tachycardia and fibrillation

Discrete delays in physiological systems. The Glass–Mackey model of respiration. Regulation of stem cell and blood cell production. Dynamical diseases.

The principal text is:

1. J. Keener and J. Sneyd, Mathematical Physiology (Springer-Verlag, 1998). Chs. 1, 4, 5, 9–12, 14–17. [Or: Second edition Vol I: Chs. 1, 2, 4, 5, 6, 7. Vol II: Chs. 11, 13, 14. (Springer-Verlag, 2009)]

Subsidiary mathematical texts are:

1. J. D. Murray, Mathematical Biology (Springer-Verlag, 2nd ed., 1993). [Third edition, Vols I and II, (Springer-Verlag, 2003).]
2. L. A. Segel, Modeling Dynamic Phenomena in Molecular and Cellular Biology (Cambridge University Press, 1984).
3. L. Glass and M. C. Mackey, From Clocks to Chaos (Princeton University Press, 1988).
4. P. Grindrod, Patterns and Waves (oup, 1991).

General physiology texts are:

1. R. M. Berne and M. N. Levy, Principles of Physiology (2nd ed., Mosby, St. Louis, 1996).
2. J. R. Levick, An Introduction to Cardiovascular Physiology (3rd ed. Butterworth–Heinemann, Oxford, 2000).
3. A. C. Guyton and J. E. Hall, Textbook of Medical Physiology (10th ed., W. B. Saunders Co., Philadelphia, 2000).